Array for achromatic imaging of a pulsed particle ensemble

ABSTRACT

An array for achromatic imaging of a pulsed ensemble of charged particles is described. The device comprises an imaging system with a round lens optics ( 2, 7 ), a low-energy drift space ( 3 ) and an accelerator ( 4 - 6 ) driven by at least one rapidly switchable voltage U(t), such that the velocity and/or trajectory of the particles in the ensemble is influenced and the particles starting from point ( 1 ) with different energies are crossing the image plane in one point ( 8 ), i.e. the chromatic aberration of the optics is compensated.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims Priority from German Application No. DE102 17 507.1 filed on Apr. 19, 2002.

FIELD OF THE INVENTION

[0002] The present invention describes an array imaging a pulsedparticle ensemble emitted from at least one point on a sample on to adetector.

[0003] It is known that so-called particle lenses, i.e. lenses forcharged particles like electrons can influence the paths of theseparticles in a similar way as an optical lens influences photon rays.

[0004] Such particle lenses are applied e.g. in electron microscopes.The chromatic and spherical aberrations of particle lenses are the mainfactors limiting spatial resolution. Astigmatism is the result ofmisalignment and can be compensated by electric or magnetic stigmatorsand coma and image curvature are often of secondary importance. However,the chromatic and spherical aberrations constitute a basic problem forall optical systems composed of round lenses.

[0005] The chromatic aberration is caused by the different energies ofthe particles in the beam and results in the fact that particles ofdifferent energy do not intersect the ideal image point. In other words:due to the chromatic aberration particles with different energy hit theimage plane in different positions.

[0006] In contrast to photon optics these aberrations cannot becorrected by suitable lens combinations. The reason is that, independentof type and geometry of the selected lens, all particle optical roundlenses are characterized by spherical and chromatic aberrationcoefficients c

and c_(c), respectively, that are always positive. Thus, the combinationof lenses with coefficients with different sign in a lens system ofround lenses is impossible.

DESCRIPTION OF THE PRIOR ART

[0007] This fundamental property of all optical round lenses forparticles is known as Scherzer's theorem [O. Scherzer, Z. für Physik 101(1936) 593].

[0008] Scherzer [O. Scherzer, Optik 2, 115 (1947)] and other authorshave searched for ways to circumvent this theorem and discusseddifferent possibilities for the correction of c

and c_(c).

[0009] An overview is given by Hawkes and Kasper [Principles of ElectronOptics, Academic Press 1996, Vol. 2, p. 857ff]. The conditions for thevalidity of Scherzer's theorem are: round lenses, real images, staticfields, no space charge, no potential jumps. These conditions implypossibilities to circumvent the theorem. Despite numerous attempts withdifferent methods, only the use of multipole correctors inhigh-resolution transmission electron microscopes has been successful upto now [M. Haider, S. Uhlemann, B. Schwan, H. Rose, B. Kabius, K. Urban,Nature 392 (1998) 768]. A second possibility of aberration correction bymeans of electron mirrors was proposed and is being tested [G. F.Rempfer et al., Microsc. Microanal. 3 (1997) 14; R. Fink et al., Journalof El. Spectrosc. Relat. Phenom. 84 (1997) 231]. These methods pose ahigh challenge on the mechanical precision and the current or voltagestability of the electronics. In addition, the adjustment is verydemanding, in particular in the case of the non-linear optical axisconnected with the solution of the electron mirror.

[0010] Several authors discussed the application of so-calledhigh-frequency lenses [Hawkes and Kasper, Principles of Electron Optics,Academic Press 1996, Vol. 2, p. 872 ff], where the lens is formed by amicro wave resonator or the resonator is integrated into a lens. Itturned out that the phase condition (i.e., the relation between thephase of the micro wave and the phase of the electron bunch whenentering the resonator) and the dwell time in the resonator plays acrucial roll. None of the proposals in connection with high-frequencylenses has been realized successfully.

[0011] In reference /1/ a particle source is described that produces apulsed particle beam in a way that the particles belonging to a bunchexperience a pulsed electrical field in a so-called “buncher”synchronized with the pulses. This pulsed electrical field causes anacceleration of the electrons at the end of the bunch. This accelerationcauses a desired shortening of the axial expansion of the particleformation. This axial compression can be used for imaging with reducedchromatic aberration. This energy focussing effect using a pulsed axialelectrical field is also known from time-of-flight mass spectroscopy[cf. /4/, section on time-lag energy focussing, p. 1154]. The reductionof flight-time differences by pulsed fields can also be exploited for animprovement of the mass resolution of a time-of-flight massspectrometer, cf. /2/. These methods cause a temporal and spatialcompression of the particle ensemble at the target (called bunchingeffect in reference /1/).

[0012] The contribution of the chromatic aberration to the totalresolution of an optical system is given by

δ_(c) =c _(c) αΔE/E

[0013] where c_(c) is the chromatic aberration coefficient dependent onlens geometry and energy, α is the beam pencil angle accepted by thecontrast aperture and ΔE/E is the relative width of the energydistribution of the imaged charged particles with centre of gravity atenergy E.

BRIEF SUMMARY OF THE INVENTION

[0014] It is an object of the present invention to provide a device thatenables correction of the chromatic aberration of a system of roundlenses for charged particles, but wherein the complexity of thearrangement is greatly reduced. This is achieved via energy dependentaxial expansion, i.e. energetic dispersion, of the pulsed particleensemble in a low-energy drift space.

[0015] According to a first aspect of the present invention, anarrangement for imaging of a pulsed particle ensemble from a sample to adetector with minimized chromatic aberration comprises: an imagingsystem with particle optical round lens optics, a low-energy part of theoptics called drift space, means for application of a rapidly switchedvoltage such that the velocity of the particles of the ensemble ischanged in a way that the particle rays starting in one point on thesample intersect the image plane in one point thus leading to areduction of the chromatic aberration in the image. To achieve this, thefastest particles reach the end of the drift space before the switchingof the electrical field and are thus not influenced by the field. Theslower particles, however, are accelerated by the application of asuitable voltage in a way that the energy gain is proportional to thelocal potential in the moment when the voltage is switched on. Theirenergy gain is the higher, the slower the particle has been on its waythrough the round lens optics. This means that the particles at thefront of the ensemble retain their energy, whereas the particles in thecentre of the ensemble gain a higher kinetic energy and the particles atthe end of the ensemble gain the highest kinetic energy.

[0016] The energy distribution of the particle ensemble can be invertedif a parabolic potential is applied. As the originally fastest particlesretain their velocity or energy, however the slowest particles are alsoaccelerated to a new energy higher than the originally fastestparticles, the chromatic aberration of the following round lens opticcan compensate the chromatic aberration of the preceding part of theoptics. The particles are intersecting in the same image point, i.e. thetotal chromatic aberration vanishes in the sense that all particle raysintersect in the ideal image point. This implies that the voltage has tobe switched in the moment when the particle ensemble is in theaccelerator at the end of the drift space. Further advantages aredescribed in the Claims.

[0017] According to a special embodiment of this first aspect of theinvention, the particles in a particle ensemble can be decelerated by aretarding voltage and dispersed in a subsequent low-energy drift spacesuch that the distance between particles with different energies isincreased. This deceleration of the particles by means of the toretarding voltage retains the velocity differences between the differentparticles but reduces the average velocity of the ensemble. Hence,electrons with different velocities gain distance from each other.Behind the drift space the particles experience an energy increase inthe pulsed accelerator such that the slower particles gain more velocitythan the faster ones. Consequently, all particle rays intersect in theideal image point leading to a vanishing chromatic aberration asdescribed above.

[0018] According to a second aspect of the present invention, anarrangement for imaging of a pulsed particle ensemble from at least onepoint of several points on a sample comprises: an imaging system withparticle optical round lens optics, a low-energy drift space increasingthe spatial and temporal distance between the particles of the particleensemble with different velocities such that after passing of theparticles through the drift space the refractive power of the round lensoptics behind the drift space is adapted at each moment such that thefocal width of the optics remains the same for all particle energies andsuch that all particle energies of the ensemble are imaged with the samemagnification on the screen. Consequently, the chromatic aberration iseliminated in the image.

[0019] Further advantages of this second aspect of the present inventionare described in the Claims.

[0020] The visualization of the particle-optical image requires adetector. Such a detector can comprise a fluorescent screen and aCCD-camera that acquires the image. Alternatively, the detector can bedesigned such that all particles are individually detected andregistered with respect to their spatial coordinate and arrival time onthe detector. This bears a number of advantages: it provides the mode ofenergy-resolved imaging of the particles or the possibility of imagingof selected particle energies such that the partial images correspondingto different energies can be adjusted in scale resulting in a sharpimage. The adjustment of the partial images taken at different energiesto the same scale requires compression, expansion, rotation ordisplacement of each partial image by means of suitable imageacquisition software. Furthermore, this procedure allows compensatingthe influence of spurious stray fields.

[0021] Of particular advantage is the application of both aspects of thepresent patent in an arrangement imaging pulsed particle ensemblesemitted from a sample in an electron or an ion microscope or in opticsfor projection lithography. It can also be exploited in the generationof pulsed electron or ion microprobes.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

[0022] In the following, the invention will be described in more detailwith reference to the accompanying Figures, in which:

[0023]FIG. 1 is a schematic drawing of the corrector;

[0024]FIGS. 2a-c shows the accelerator inverting the energy distributionwith the transmitted particle ensemble at three different times;

[0025]FIG. 3 is a schematic drawing of the energy-versus-pathdistribution of the particles within the round lens optics or the columnof the microscope.

DETAILED DESCRIPTION OF THE INVENTION

[0026] Referring to FIGS. 1 and 2, a preferred embodiment of the imagingdevice in accordance with the invention is a particle optical round lenssystem including a low-energy drift space and an electrostaticaccelerator such that a rapidly switched axial electric field induces aninversion of the energy distribution of the particles. Particles withenergy E₀ are focussed to the correct image plane. Without corrector,particles with higher energy are deflected too weakly by the roundlenses. Hence, their focal plane is shifted to higher z-values along theoptical axis. The corresponding chromatic aberration coefficient c_(c)is thus always positive. In contrast to photon optics, this is thereason that no achromatic optical round lens system for chargedparticles can be constructed.

[0027] In FIG. 1 the accelerator consisting of electrodes 4, 5 and 6 isinserted between lens 2, drift tube 3 and lens 7. The operatingprinciple exploits that a particle ensemble with an energy width •E isexpanded in a low-energy drift space 3 as a consequence of the differentvelocities of the particles (dispersion). This dispersion is linear invelocity v, i.e. quadratic in energy (E=mv²/2). After passing the driftspace the particles have a spatial distribution as shown in FIG. 2a. Thefastest particles 10 with energy E₀ define the front side of theensemble, particles 11 correspond to an average energy and the slowestparticles 12 with energy E₀−•E define the end of the ensemble. Thisspatial configuration of the particles resulting from the dispersioneffect enters the accelerator through entrance electrode 4. At theswitching time t=t

the ensemble is completely inside of the accelerator, as shown in FIG.2b. At this moment the voltage U(t) at the entrance electrode 4 israpidly varied by the value •U, i.e. to negative or positive values forelectrons or for positively charged ions, respectively. This voltagegives rise to the electrical field F. Its propagation with the speed oflight can be neglected in comparison with the relevant flight times ofthe particles. Further consideration reveals that an axial change of theelectrical field is connected with a ring-shaped magnetic field. Incontrast to magnetostatic lenses this causes no energy-dependent imagerotation. This is an advantage of the device even at extremely highfrequencies.

[0028] Calculations reveal that in the case of rapidly switchedelectrostatic lenses an additional lens action arises due to the inducedmagnetic ring field. At typical switching times and geometries, thislens action can be neglected in comparison with the electrostatic lensaction.

[0029] The fastest particles 10, i.e. those particles that have reachedthe centre of the exit electrode 6, cf. FIG. 2b, are not influenced bythe electric field. However, the slower particles 11 and 12 experiencean energy gain during their travel through the remaining part of theaccelerator. This energy gain is defined by the local potential at themoment t=t

. We consider the example •U=2•E/e. In this case the slowest particles12 that have reached the plane of the entrance electrode 4 at theswitching time t=t₀, are lifted by the energy value 2•E, because theyhave to travel along the complete accelerating field. Analogously, thecentre particles 11 are accelerated by a smaller energy value, sincethey travel only across the second half of the accelerating field. Afterleaving the accelerator, cf. FIG. 2c, the energy distribution is thusinverted. The particles at the front of the bunch 10 have the unchangedenergy E₀, the particles in the centre of the bunch 11 have a higherenergy and the particles at the end of the bunch 12 have the new energyE₀+•E.

[0030] Variation of the voltage jump •U facilitates a non-symmetricalinversion of the energy distribution behind the drift space, i.e. thenew energy of particles 12 is E₀+x•E. This case can he advantageous fora given lens configuration. Furthermore, the example shown in FIG. 2b,where the particle ensemble fills the whole accelerator at the time t=t

is no necessary condition of the method. In each case, however, theinitially slowest particles 12 are the fastest particles after passingthe accelerator. The electrode arrangement 5 serves for fringe-fieldcorrection. In the common way for electrostatic accelerators theseelectrodes define the desired voltage drop, e.g. by means of a resistorchain connecting the electrodes with each other and with the ends of theaccelerator, i.e. electrodes 4 and 6. The accelerating field can beparabolic in a preferred embodiment. Alternatively, in order to obtainbetter particle optical properties, it can deviate from this simplestructure by means of suitably shaped electrodes and by the temporalbehavior of the voltage rise. For the basic operation of the acceleratorthe exact shape of the field is of secondary importance.

[0031]FIG. 1 shows a preferred embodiment of the chromatic corrector ina particle optical system consisting of two converging lenses 2 and 7.In this example the particle ensemble starting from the source point 1is converted to an approximately parallel beam by the first lens 2. Inthe drift space 3 the ensemble is expanded due to its energy width •Ebefore it passes the accelerator consisting of entrance electrode 4,correction electrodes 5 and exit electrode 6, followed by the secondlens 7 that focuses the ensemble to the image point 8. As a consequenceof the chromatic aberration of the first lens 2 the low-energy particles(dashed trajectories) are retracted more strongly than the high-energyparticles (solid trajectories). Owing to the inversion of the energydistribution of the particles when passing the accelerator as describedabove, the initially low-energy particles are converted to thehigh-energy particles, as indicated by interchanging the full and dashedtrajectories. The second lens 7 again acts more strongly on thelow-energy particles due to its chromatic aberration, such that now thechromatic aberration of the first lens 2 is compensated. Alltrajectories cross in the ideal image point 8. Without correction, theinner rays always correspond to the low-energy particles and the secondlens 7 again acts more strongly on these particles, resulting in thedotted trajectories. The sum of lens 2 and lens 7 exhibits a significantchromatic aberration without corrector (image points 8 and 9) and noaberration with active corrector (only 8).

[0032]FIG. 3 further illustrates the preferred embodiment of theinvention by means of a schematic diagram of the energy-versus-opticalpath distribution. The ensemble starting from the sample 13 istransported by the round lens optics 14, then decelerated in theretarding space 15, then axially expanded in the drift space 16 suchthat the expanded ensemble 21 enters the accelerator 17 at the end ofthe drift space. The switched voltage in the accelerator 17 lifts thelow-energy part of the particle ensemble, resulting in an inversion ofits energy distribution, see distribution 22. The final part of theimaging optics 18 utilizes this inversion for the correction of thechromatic aberration such that a sharp image appears on the detector 19.

List of Numerals

[0033]1. Source point

[0034]2. First lens

[0035]3. Low-energy drift space

[0036]4. Entrance electrode of the accelerator

[0037]5. Corrector electrodes of the accelerator

[0038]6. Exit electrode of the accelerator

[0039]7. Second lens

[0040]8. Image point of all particles with active corrector

[0041]9. Image point of the slowest particles without corrector

[0042]10. Particles with maximum energy before correction

[0043]11. Particles with medium energy before correction

[0044]12 Particles with lowest energy before correction

[0045]13. Position of the sample

[0046]14. First imaging optics

[0047]15. Deceleration optics

[0048]16. Low-energy drift space

[0049]17. Rapidly switchable accelerator

[0050]18. Second imaging optics

[0051]19. Image plane with detector

[0052]20. Energy-versus-path distribution of the particles at the sample

[0053]21. Energy-versus-path distribution of the particles before theinversion

[0054]22. Energy-versus-path distribution of the particles after theinversion U(t) pulsed voltage

We claim:
 1. An array for achromatic imaging of a pulsed particleensemble comprising: means for imaging containing at least twoparticle-optical round lenses 2, 7, a low-energy drift space 3 thatgives rise to an energy-dependent axial expansion of the particleensemble and means for changing the energy distribution of the particleensemble located between the drift space and the second lens 7 such thatan electrode arrangement (4, 5, 6) facilitates the generation of apulsed axial electric field.
 2. An array according to claim 1 in whichthe particles within the particle ensemble are decelerated by aretarding voltage before entering the drift space.
 3. An array accordingto claim 1 in which the energy distribution of the particle ensemble isinverted by a rapidly switchable voltage.
 4. An array according to claim1 in which the energy distribution of the particle ensemble is invertedexcept for a scaling factor by means of a rapidly switchable voltage. 5.An array according to claim 1 in that the particle ensemble 13 isemitted from a sample to a detector.
 6. An array for achromatic imagingof a pulsed particle ensemble comprising: an imaging system with atleast one particle optical round lens (7), a preceding low-energy driftspace (3) for energy-dependent axial expansion of the particle ensemble,such that the focal width of the round lens (7) is actively variedduring the passage of the particle ensemble such that well-focusedimaging is obtained for all particle energies.
 7. An array according toclaim 6 in which the round-lens optics is actively varied such that allparticle energies of the ensemble are imaged to the screen withidentical magnification.
 8. An array according to claim 6 in which thepartial images corresponding to different particle energies areseparately recorded and are adjusted to each other by means of numericalprocedures.
 9. An array according to claim 6 in which the detector is afluorescent screen.
 10. An array according to claim 6 in which thedetector selects a time window out of the particle ensemble being imagedsuch that the pulse length is restricted and the aberrations can becorrected.
 11. An array according to claim 6 in which the detectorregisters the space coordinate and arrival time of the particlesindividually.
 12. An array according to claim 6 in which the detector isa CCD-camera.
 13. An array according to claims 1 or 6 in which theparticles are electrons or ions.
 14. An array according to claim 1 or 6that is part of an electron microscope, an ion microscope, an instrumentfor projection lithography or an electron- or ion-microprobe.
 15. Anarray according to claim 6 in that the particle ensemble 13 is emittedfrom a sample to a detector.